Among the electric motor drives, permanent magnet linear motors (PMLM) are probably the most naturally suited to applications involving high speed and high precision motion control. The increasingly widespread industrial applications of PMLMs in various semiconductor processes, precision metrology and miniature system assembly are self-evident testimonies of the effectiveness of PMLMs in addressing the high requirements associated with these application areas. The main benefits of a PMLM include the high force density achievable, low thermal losses and, most importantly, the high precision and accuracy associated with the simplicity in mechanical structure. Unlike rotary machines, linear motors require no indirect coupling mechanisms as in gear box, chain and screw couplings. This greatly reduces the effects of contact-type non-linearities and disturbances such as backlash and frictional forces, especially when they are used with aerostatic or magnetic bearings. However, the advantages of using mechanical transmission are also consequently lost, such as the inherent ability to reduce the effects of model uncertainties and external disturbances. Therefore, a reduction of these effects, either through proper physical design or via the control system, is of paramount importance if high-speed and high precision motion control is to be achieved.
A significant and well-known nonlinear effect in the dynamics of the PMLM is the phenomenon of force ripple arising from the magnetic structure which exhibit characteristics that are position and velocity dependent. This is a prominent factor limiting the performance of PMLMs. Periodic disturbances also occur in a variety of engineering applications. In data storage systems, for example, the eccentricity of the track on a disk requires a periodic movement of the read/write head at the frequency of the rotation of the disk. In the rotary type DC motors and stepper motors, torque pulsations occur at the frequency of rotation of the motors, due to the tendency of the permanent magnets to align themselves along directions of minimum reluctance. In switched reluctance motors, torque ripples also arise due to the saturation effect and the variation of magnetic reluctance leading to highly nonlinear characteristics which result in the ripples.
A great deal of effort has been devoted to overcome the difficulties associated with the nonlinear rippling effects. Among the prior art, H∞ optimal feedback control has been suggested to provide a high dynamic stiffness to external disturbances (D. M. Alter and T. C. Tsao, Control of linear motors for machine tool feed drives: design and implementation of H∞ optimal feedback control ASME J. of Dynamic systems. Measurement and Control, vol. 118, pp649-658, 1996). A neural-network feed-forward controller has also been proposed to reduce positional inaccuracy due to reproducible and slowly time-varying disturbances (G. Otten, T. J. A. de Vries, J. van Amerongen, A. M. Rankers and E. W. Gaal, Linear motor motion control using a learning forward controller, IEEE/ASME Trans. on Mechatronics, vol.2(3), pp179-187, 1997). Yao and Tomizuka have proposed an adaptive robust control approach and applied it subsequently to high speed, high accuracy motion control of machine tools (B. Yao and M. Tomizuka, Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form, Automatica, vol. 33(5), pp.893-900, 1997.). A radial-basis function has been proposed by Tan et al as part of a composite control scheme to reduce errors arising from nonlinear uncertain remnants which were not considered in the linear control (K. K. Tan, S. N. Huang, H. F. Dou, S. Y. Lim, S. J. Chin, Adaptive Robust Motion Control for Precise Trajectory Tracking Applications, Mechatronics-submitted, 1999.). Iterative learning control has also been proposed in the past, where it has been targeted at applications involving repeated iterative operations (K. K. Tan, T. H. Lee, S. Y. Lim, and H. F. Dou, Learning enhanced motion control of permanent magnet linear motor, Proc. of the third IFAC International Workshop on Motion Control, Grenoble, France, pp397-402, 1998.). In all these works, while the efforts were geared towards the compensation of nonlinear uncertainties, there has been no explicit modelling of the ripple force phenomenon, and consequently, no direct approach to attempt to suppress these forces which should yield direct improvement in tracking performance.